1. Field of the Invention
This invention is directed to a process for substantially moiré-free halftoning color documents using combinations of cluster screens and line screens.
2. Description of Related Art
With the advent of inexpensive digital color printers, methods and systems of color digital halftoning have become increasingly important. It is well understood that most digital color printers operate in a binary mode, i.e., for each color separation, a corresponding color spot is either printed or not printed at a specified location or pixel. Digital halftoning controls the printing of color spots, where spatially averaging the printed color spots of all the color separations provides the illusion of the required continuous color tones.
The most common halftone technique is screening, which compares the required continuous color tone level of each pixel for each color separation with one of several predetermined threshold levels. The predetermined threshold levels are stored in a halftone cell, which is spatially replicated and tiled to form a halftone screen that is the size of a given image. If the required color tone level is darker than the threshold halftone level, a color spot is printed at the specified pixel. Otherwise the color spot is not printed. It is understood in the art that the distribution of printed pixels depends on the design of the halftone cell. For cluster halftone cells, all printed pixels are grouped into one or more clusters. If a cluster-halftone cell only generates a single cluster, it is referred to as a single-center halftone screen, a single-dot halftone cell, a single-cell halftone dot, or some similar terminology. Alternatively, halftone cells maybe dual-dot, tri-dot, quad-dot, supercells or the like, where supercells are halftone cells with multiple dot centers used to increase the angular accuracy of the screen or the number of gray levels that the screen can produce. As is the practice in the art, the terms “cells” and “screens” are used here somewhat interchangeably.
Halftone cells are typically two-dimensional threshold arrays and are relatively small in comparison to the overall image or document to be printed. Therefore, for a given color separation, the screening process uses an identical halftone cell to tile the complete image plane. The output of the screening process, using a single cell halftone dot, includes a pattern of multiple small “dots”, which are regularly spaced and is determined by the size and the shape of the halftone cell. Typically, the shape and tiling geometry of the halftone cell is a square, rectangle, parallelogram, line, or the like. Various digital halftone screens having different shapes and angles are described in An Optimum Algorithm for Halftone Generation for Displays and Hard Copies, by T. M. Holladay, Proc. Soc. for Information Display, 21, p. 185 (1980). Hexagonal tiling has also been in employed in the halftoning art. The screening output, for square, rectangular or parallelogram tiling as a two-dimensionally repeated pattern, possesses two fundamental spatial frequency vectors, which are completely defined by the geometry of the halftone cell.
A common problem that arises in digital color halftoning is the occurrence of moiré patterns. Moiré patterns are undesirable interference patterns that occur when two or more color halftone separations are printed over each other. Since color mixing during the printing process is a non-linear process, frequency components other than the fundamental frequencies of the two or more color halftone separations can occur in the final printout. For example, if an identical halftone screen is used for two color separations, theoretically, there should be no moiré patterns. However, any slight misalignment between the two color halftone separations occurring from an angular difference and/or a scalar difference will result in two slightly different fundamental frequencies, which will be visibly evident as a very pronounced moiré interference pattern in the output. To avoid, for example, two-color moiré patterns due to misalignment, or for other reasons, different halftone screens are commonly used for different color separations, where the fundamental frequency vectors of the different halftone screens are separated by relatively large angles. Therefore, the frequency difference between any two fundamental frequencies of the different screens will be large enough so that no visibly noticeable moiré patterns are produced.
In selecting different halftone screens, for example, for three color separations, it is desirable to avoid any two-color moiré as well as any three-color moiré. It is well known that in the traditional printing industry that three halftone screens, constructed of cells which are square in shape and identical, can be placed at 15°, 45° and 75°, respectively, from a point of origin, to provide the classical three-color moiré-free solution. This is described in Principles of Color Reproduction, by J. A. G. Yule, John Wiley & Sons. N.Y. 1967.
However, for digital halftoning, the freedom to rotate a halftone screen is limited by the raster structure, which defines the position of each pixel. Since tan(15°) and tan(75°) are irrational numbers, rotating a halftone screen to 15° or 75° cannot be exactly implemented in digital halftoning. To this end, some methods have been proposed to provide approximate instead of exact moiré-free solutions. For example, in U.S. Pat. Nos. 5,323,245 and 5,583,660, this problem is approached by using a combination of two or more perpendicular, unequal frequency screen patterns and non-perpendicular, equal frequency non-conventional screen patterns. However, all these approximate solutions result in some halftone dots having centers that do not lie directly on addressable points, or on the pixel positions defined by the raster structure. Therefore, the shape and center location varies from one halftone dot to another. Consequently, additional interference or moiré between the screen frequencies and the raster frequency can occur. In another approach, U.S. Pat. No. 5,371,612 discloses a moiré prevention method to determine screen angles and sizes that is usable solely for square-shaped, halftone screens.
Other factors that limit the usefulness of the traditional 15, 45, 75-degree screen angle alignments in, for example, a xerographic environment, are process effects, such as, for example, the effects of development order and the so-called dual beam effect. Development order effects moiré when a first colorant interacts with the deposition of a second colorant. The interaction can contribute to an increased perceptibility of moiré. The dual beam effect can add frequency components to an image that beat with halftone screens and lead to moiré. The dual beam effect can occur where two or more beams are used to paint an image. For example, a slight spacing error or misalignment between two laser beams can create a periodic pattern such as a set of two lines that are close together and separated by a gap from a next set of close lines. This pattern possesses frequency components that can beat with the halftone screens to generate moiré. Other sources of error within printing devices that generate additional frequency components include photoreceptor velocity nonuniformity, mirror wobble, and raster start position jitter. In order to address these problems and others, screening techniques are desired that are robust and tolerant of the use of multiple beams, additional frequency components from other sources in the image writing and marking process, and colorant development order effects.